Here we investigate GL of black holes in Einstein Quartic Gravity (EQG), the next simplest GQTG after Einsteinian cubic gravity (ECG) [1]}.
Although the systematic construction of actions that are \(n\) -th order in curvature from lower order ones via
recursive formulas have been obtained that allow for construction of any GQTG
[2]}, EQGs have the highest degree of curvature possible that allows for an analytic solution of the near horizon equations for the temperature and mass in terms of the horizon radius \(r_+\) . As such they are of particular interest and merit further study.
We also note that the EQG theory we study does not meet the general criteria used to construct an alternative class of “Einsteinian" higher-curvature theories [3]} (though its cubic counterpart [4]} satisfies these criteria), apart from a particular quartic GQTG. We therefore expect that some combination of the EQG invariants we consider (perhaps with some possibly trivial densities) could satisfy these other criteria.
